A functional model of a simplified clarinet

Abstract

A functional model (computer simulation) of a simplified clarinet has been implemented on a digital computer. The simplified clarinet consists of a standard clarinet mouthpiece and reed attached to a straight cylindrical tube without tone holes. The tube and mouthpiece are represented in the model by a lumped element approximation to a transmission line. Application of Kirchoff's circuit laws to this circuit gives a coupled set of differential equations which were solved numerically on a digital computer to yield volume velocities and pressures in the mouthpiece and tube. The pressure in the mouthpiece drives the reed which is represented in the model as a tapered bar clamped at one end. The partial differential equation describing vibrations of such a bar was solved numerically to obtain the size and shape of the reed aperture. The reed aperture area governs the volume velocity into the tube which in turn drives the air column vibrations. The model exhibits self‐sustained oscillations, threshold blowing pressures, and “lipping” of the tone. The spectra of the mouthpiece and radiated pressures are in general agreement with actual clarinet spectra. Some interesting features of the model are the inclusion of a frequency‐dependent viscous loss in the tube and a dependence of the aperture volume velocity on the initial or rest opening of the aperture.